Question: Which of the following numbers is a factor of 77? ${4,5,6,11,13}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $77$ by each of our answer choices. $77 \div 4 = 19\text{ R }1$ $77 \div 5 = 15\text{ R }2$ $77 \div 6 = 12\text{ R }5$ $77 \div 11 = 7$ $77 \div 13 = 5\text{ R }12$ The only answer choice that divides into $77$ with no remainder is $11$ $ 7$ $11$ $77$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $77$ $77 = 7\times11 11 = 11$ Therefore the only factor of $77$ out of our choices is $11$. We can say that $77$ is divisible by $11$.